Eagles or A Long walk

An idea spawned off the ending of the “Lord Of The Rings: Return of The King” written by J.R.R. Tolkien when Gandalf called upon the Great Eagles that swooped in to save the fellowship from their molten demise. The argument that has been placed upon the Lotr fandom, why couldn’t the Great Eagles have taken Frodo to Mt. Doom to save th fellowship from the Long journey, allowing Frodo the chance to not be Consumed by the power the ring has to offer.

Premise 1: The great Eagles are too proud to serve the fellowship as a taxi
Premise 2: Gwaihir is a Maia spirit because of Gandalf
Premise 3: By Valar law, Gandalf would have to tell the great eagle that he is in possession of the ring.
Conclusion : Gandalf didn’t call upon the Eagles because he’d have to tell the Eagles about the ring and gandalf believed they might take the ring for their own power.